To analyze socioeconomic gradients in TVIP scores, we construct country- specifi c, age- specifi c z- scores by subtracting the month- of- age- specifi c mean of the raw score
and dividing by the month- of- age- specifi c standard deviation, separately by country and by urban- rural place of residence as in Cunha and Heckman 2007 and many
others. As a robustness test, we also report results that use the tables given by the test developers to standardize the test as done by Paxson and Schady 2007.
A fraction of children in every survey, ranging from 2 percent in Colombia to 18 percent in Nicaragua, did not take the TVIP. Although we do not have data that are comparable
across all fi ve countries on the reasons why these children did not take the test, it appears that most of them had diffi culty understanding the instructions and making it past the
practice items that are applied at the outset. Consistent with this, there are more children with missing test data at younger ages and more in the poorest country, Nicaragua. Earlier
work on Ecuador has shown that children who miss a given test do worse on other tests, or on the same test in different survey waves, than other children with comparable wealth
and parental schooling levels Paxson and Schady 2010; Schady 2011. Because children who miss tests are likely to be “low performers,” we assign these children a test score of
zero. We test the robustness of our results to this approach to handling missing data.
We construct a measure of household wealth by aggregating a number of household assets and dwelling characteristics using the fi rst principal component. Similar wealth
indices have been used extensively in the medical, demographic, nutritional, and eco- nomics literatures. The exact variables included in the wealth measures vary by coun-
try because of differences in the assets and dwelling characteristics that were collected in the surveys see online Appendix Table 1 at http:uwpress.wisc.edujournals. As
a robustness check, we test whether our results are sensitive to using consumption or education as an alternative measure of socioeconomic status, or to using only a com-
mon set of assets to construct the wealth index in all countries.
There are substantial differences across the countries we study in their level of de- velopment. Chile is the richest of the fi ve countries, with GDP per capita, adjusted for
Purchasing Power Parity PPP in 2012, above US22,000, and Nicaragua is the poor- est, with GDP per capita equal to US 4,006. The other three countries—Colombia, Ec-
uador, and Peru—all have per capita GDP levels between US9,500 and US11,000.
3
The average grades of completed schooling of adults in each country follows the same pattern as GDP per capita, with approximately seven more grades of schooling in Chile
than in Nicaragua. Like other countries in Latin America, the countries we analyze are highly unequal. The Gini coeffi cient of household per capita income ranges from 0.48
for Peru to 0.56 for Colombia. In comparison, the Gini coeffi cient for Sweden is 0.25 and that for the United States is 0.41. The average Gini for OECD countries excluding
the two Latin American countries, Chile and Mexico is 0.31.
III. Results
The aim of this paper is descriptive. In our main results, we simply compare the TVIP scores for children in the top and bottom quartiles of the distribu-
3. The World Bank classifi es Chile as a high-income country; Colombia, Ecuador, and Peru as upper-middle income countries; and Nicaragua as a lower-middle-income country.
tion of wealth. Because associations between TVIP scores and wealth could differ be- tween urban and rural areas, we calculate separate wealth indices and conduct separate
analyses for urban and rural areas. Table 2 shows that differences in language development between richer and poorer
children within countries are statistically signifi cant and large.
4
Differences across quartiles are biggest in urban Colombia 1.23 standard deviations and rural Ecuador
1.21 standard deviations. Online Appendix Table 2 shows that, as expected, the dif- ferences between children in the richest and poorest deciles as opposed to quartiles
are substantially larger—in both urban Colombia and rural Ecuador they are 1.64 standard deviations.
We next present the results from nonparametric Fan regressions Fan and Gijbels 1996 of the difference in scores between children in the top and bottom quartiles,
and the associated confi dence intervals constructed by bootstrapping. Figure 1 sug- gests that the bulk of the difference between poorer and less- poor children is apparent
by age three in all countries; Appendix Figure 2 shows that this is also the case in comparisons between the poorest and richest deciles. We note, however, that making
comparisons of age gaps in test scores measured in standard deviations is not straight- forward when the tests are measured with error. Suppose, as seems likely, that there is
more measurement error in the TVIP at younger ages for example, if younger children are more easily distracted. In this case, a fi nding of a constant gap in standard devia-
tions of test scores as children age would be consistent with a decline in the actual as opposed to measured gap as children age.
5
We conduct a number of robustness checks on our main results Table 3. First, for four countries Colombia, Ecuador, Nicaragua, and Peru, we present results in which
we use a common set of household assets rather than the largest set of assets available in the surveys for each country to construct our measure of wealth. We cannot do
this for Chile because there are very few assets that are common to the Chilean and other data sets. Second, for two countries in which consumption data are available
Colombia and Nicaragua, we sort households into quartiles using household per capita consumption rather than wealth. Third, we compare outcomes for children of
mothers with incomplete primary education or less and those with complete secondary education or more. Fourth, we restrict the sample to children of monolingual parents.
6
4. There are substantial differences across countries in the age distribution of the sample, even for countries where nominally the coverage is the same Colombia, Ecuador, Nicaragua. To ensure that any comparisons
we make across countries are not affected by differences in the age composition of children, all of the results we report give equal weight to each month of age, within a country, and by place of residence urban or rural.
In practice, the unweighted results are very similar to those that use these weights. The t-statistics adjust for the possible correlation of errors at the level of communities or census tract in Colombia, Ecuador, Nicaragua,
and Peru, and at the region level in Chile. 5. We thank an anonymous referee for pointing this out to us.
6. In Peru, the TVIP was translated into Quechua, an indigenous language spoken primarily in rural areas of the highlands, and children were given the option of taking the test in Spanish or Quechua. Twenty-two
percent of children in rural areas, but only 0.1 percent of children in urban areas, chose to take the test in Quechua. Because children in households that speak Quechua or another indigenous language may have more
limited vocabularies in any given language, and because the likelihood of being a non-Spanish speaker is correlated with household wealth, we exclude children with mothers who report they speak a language other
than Spanish in Peru 56 percent and 17 percent in rural and urban areas, respectively and Ecuador 2 percent in both urban and rural areas.
T he
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Table 2 Main Results
Chile Colombia
Ecuador Nicaragua
Peru Urban
Rural Urban Rural Urban
Rural Rural
Urban Rural
Richest quartile 0.42
0.47 0.77
0.25 0.46
0.63 0.52
0.50 0.43
Wealth quartile Poorest quartile
–0.36 –0.42
–0.46 –0.32
–0.41 –0.58
–0.25 –0.45
–0.35 Difference
0.78 0.89
1.23 0.57
0.87 1.21
0.77 0.95
0.77 t
- statistic 12.28
7.64 13.96
7.58 9.41
8.27 6.51
8.12 5.29
Notes: Clustering of standard errors is done at community or census tract level Colombia, Ecuador, Nicaragua, Peru and region level Chile. The calculation of the mean scores gives equal weight to each month of age, within a country, and by place of residence urban or rural.
S cha
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Chile
1.5 1.2
.9 .6
.3 –.3
–.6 –.9
–1.2 –1.5
36 42 48 54 60 66 72 1.5
1.2 .9
.6 .3
–.3 –.6
–.9 –1.2
–1.5 36 42 48 54 60 66 72
1.5 1.2
.9 .6
.3 –.3
–.6 –.9
–1.2 –1.5
36 42 48 54 60 66 72 1.5
1.2 .9
.6 .3
–.3 –.6
–.9 –1.2
–1.5 36 42 48 54 60 66 72
1.5 1.2
.9 .6
.3 –.3
–.6 –.9
–1.2 –1.5
36 42 48 54 60 66 72
1.5 1.2
.9 .6
.3 –.3
–.6 –.9
–1.2 –1.5
36 42 48 54 60 66 72 1.5
1.2 .9
.6 .3
–.3 –.6
–.9 –1.2
–1.5 36 42 48 54 60 66 72
1.5 1.2
.9 .6
.3 –.3
–.6 –.9
–1.2 –1.5
36 42 48 54 60 66 72 1.5
1.2 .9
.6 .3
–.3 –.6
–.9 –1.2
–1.5 36 42 48 54 60 66 72
Age in Months Age in Months
Age in Months Age in Months
Age in Months
Age in Months Age in Months
1st poorest quartile 4th richest quartile
95 CI 95 CI
Age in Months Age in Months
Colombia Ecuador
Rural Areas
Nicaragua Peru
Chile Colombia
Ecuador
Urban Areas
Peru
Figure 1 Age Patterns in Scores
Notes: Nonparametric regressions of average TVIP score on age in months, by wealth quartile. The bandwidth of the regressions is 7.5.
Table 3 Robustness Checks and Extensions
Chile Colombia
Ecuador Nicaragua
Peru Urban
Rural Urban Rural Urban
Rural Rural
Urban Rural
Common set of assets
a
Richest quartile 0.79
0.44 0.51
0.62 0.40
0.47 0.43
Poorest quartile –0.48
–0.25 –0.39
–0.54 –0.20
–0.56 –0.34
t - stat of difference
10.68 6.57
9.22 8.09
5.29 10.74
5.30 Consumption
Richest quartile 0.88
0.49 0.42
Poorest quartile –0.43
–0.23 –0.21
t - stat of difference
13.03 6.55
5.37 Maternal education
Highest education 0.16
0.27 0.32
0.44 0.46
0.60 1.12
0.33 0.63
Lowest education –0.52
–0.33 –0.65
–0.23 –0.42
–0.56 –0.10
–0.80 –0.15
t - stat of difference
8.97 4.14
10.48 5.04
7.40 9.20
5.58 9.52
6.08 Monolingual mothers
Richest quartile 0.46
0.63 0.52
0.48 Poorest quartile
–0.39 –0.57
–0.40 –0.47
t - stat of difference
9.05 8.30
7.52 4.44
Using external norms Richest quartile
112.36 106.70
113.30 86.92
89.29 99.02
73.03 106.82
83.55 Poorest quartile
96.65 90.32
88.55 78.29
73.62 75.08
65.62 86.99
69.20 t
- stat of difference 6.63
6.70 13.15
6.86 9.24
8.23 5.98
8.47 5.10
455 Lower and upper bound
0.43 0.41,
0.52 0.76,
0.79 0.24,
0.25 0.39,
0.61 0.57,
0.68 0.35,
0.63 0.49,
0.51 0.35,
0.51 Poorest quartile
– 0.36, – 0.40
– 0.39, – 0.46
– 0.46, – 0.47
– 0.31, – 0.32
– 0.33, – 0.46
– 0.50, – 0.60
– 0.23, – 0.36
– 0.37, – 0.47
– 0.29, – 0.43
t - stat of difference
11.40, 15.70
7.90, 7.80
13.70, 14.60
7.30, 7.60
7.30, 11.10
7.20, 8.80
5.00, 8.00
8.00, 8.50
3.80, 6.60
Notes: Clustering of standard errors is done at the community or census tract level Colombia, Ecuador, Nicaragua, Peru and region level Chile. The calculations of the mean scores give equal weight to each month of age, within a country and by place of residence urban or rural. The fraction of mothers with incomplete primary or less education is 3.5 percent for
urban Chile, 7.8 percent for rural Chile, 12.3 percent for urban Colombia, 38.5 percent for rural Colombia, 14.3 percent for urban Ecuador, 20.1 percent for rural Ecuador, 68.5 percent for rural Nicaragua, 11.1 percent for urban Peru, and 51.3 percent for rural Peru. The fraction of mothers with complete secondary education or more is 66.3 percent for urban Chile,
42.5 percent for rural Chile, 53.5 percent for urban Colombia, 14.9 percent for rural Colombia, 26.5 percent for urban Ecuador, 23.8 percent for rural Ecuador, 3.7 percent for rural Nicaragua, 56.5 percent for urban Peru, and 13 percent for rural Peru. Children of mothers who speak only Spanish account for 83 percent of the sample in urban Peru, 44.2 percent in
rural Peru, 98.7 percent in urban Ecuador, and 98.8 percent in rural Ecuador. a. Assets include: car, type of fl oor, type of walls, electricity, access to piped water, and possession of cooking stove and refrigerator.
Fifth, we report results that use the norms provided by the test developers rather than the internal z- scores we construct to standardize the TVIP.
7
Table 3 shows that the patterns summarized above are robust. Results are very simi- lar when only assets that are common across countries are used to construct the wealth
index, or when we use consumption, rather than wealth, as a measure of well- being. There are substantial differences in child TVIP scores by mother schooling levels in-
complete primary or less, compared to complete secondary or more in all countries. For example, in rural Ecuador the difference in outcomes between children of moth-
ers with complete secondary schooling or more and those with incomplete primary schooling or less is 1.16 standard deviations. Excluding children in households where
a language other than Spanish is spoken substantially increases the wealth gradient in rural Peru from 0.77 to 0.95 standard deviations but has little effect on the results for
urban Peru or urban or rural Ecuador.
Results that use the norms provided by the test developers the fi fth row of the table show similar wealth gradients as those we report in our main specifi cation. Recall that
the distributions of wealth in the data we use to calculate the TVIP scores are broadly similar to the distributions of wealth in nationally representative surveys for the rural
areas of all fi ve countries and for the urban areas of Chile and Colombia. We can there- fore also use these results to make cautious comparisons across rural- urban areas in
these two countries and across rural areas in all fi ve countries.
First, limiting the sample to rural areas, mean scores are highest in Chile 90 points, substantially lower in Colombia and Ecuador 78 and 75 points, respec-
tively, and lower still in Peru and Nicaragua 69 and 66 points, respectively. This means that, in Nicaragua and Peru, the average child in the poorest wealth quartile
in rural areas has TVIP scores that are more than two standard deviations below the reference population that was used to norm the test. The results for Peru are particu-
larly noteworthy because GDP per capita levels in Peru are roughly comparable to those found in Colombia and Ecuador and are approximately three times as high as
those in Nicaragua. Second, children in urban areas have somewhat higher scores than those in rural areas in Chile a difference of six points for those in the highest
quartile and substantially higher scores in Colombia a difference of 26 points, more than 1.5 standard deviations, for those in the highest quartile. Of course,
in interpreting these urban- rural comparisons, it is important to keep in mind that average income levels tend to be substantially higher in urban than in rural areas in
most Latin American countries.
We also test the degree to which our results are sensitive to missing test data by calculating upper and lower bounds on the wealth gradients last row of Table 3, in
the spirit of Manski 1990 and Horowitz and Manski 2000. Specifi cally, we esti- mate the upper bound by excluding all children with missing test data in the richest
wealth quartile, and assigning a score of 0 to all children in the poorest wealth quar- tile who were missing the TVIP, as before. Conversely, we estimate the lower bound
by excluding all children with missing test data in the poorest wealth quartile and assigning a score of 0 to all children in the richest wealth quartile who were missing
7. The TVIP has been standardized by the test developers on samples of Mexican and Puerto Rican chil- dren to have an average score of 100 and a standard deviation of 15 at all ages. The lowest possible standard-
ized score is 55.
the TVIP, as before. Table 3 shows that the bounds that take account of missing test data are generally quite tight. For example, in urban Chile, our basic estimate sug-
gests that the difference in outcomes between children in the top and bottom wealth quartiles is 0.78 standard deviations, the lower bound on this difference is 0.74, and
the upper bound is 0.83. Only in Nicaragua, the country with the largest number of children with missing test data, are the bounds somewhat wider, with a lower bound
for the difference of 0.58 standard deviations and an upper bound of 0.99 standard deviations.
Although the aim of our paper is descriptive, and the data we have do not allow us to establish causality from socioeconomic status whether measured by wealth,
consumption, or education to child cognitive development, we make an attempt to deepen our understanding of the gradients we observe with some conditional
associations. Specifi cally, in Table 4, we present the results from three regressions. In the fi rst, Specifi cation 1, only the dummy variable for children in the fourth
richest quartile is included as an explanatory variable; in Specifi cation 2, we add maternal schooling attainment; in Specifi cation 3, fi nally, we also add location fi xed
effects.
These results show that, by and large, the signifi cant association between wealth and child cognitive development is robust to the inclusion of these additional covari-
ates. In some cases for example, rural Colombia adding maternal schooling to the regression reduces the coeffi cient on wealth by relatively little while in others for
example, urban Peru, the coeffi cient on wealth goes down substantially. Similarly, adding location fi xed effects has a large effect on the coeffi cient on wealth in some
settings for example, urban Colombia, the urban and rural areas of Ecuador but not in others for example, the urban and rural areas of Chile and Peru. In part, this is
likely to refl ect the much larger number of location fi xed effects in some countries for example, in Colombia, the location fi xed effects correspond to municipalities in rural
areas and neighborhoods in urban areas; there are 213 and 385 location fi xed effects in urban and rural areas, respectively than in others in Chile, the location fi xed effects
correspond to much larger units, roughly comparable to states in the United States; there are 15 and 13 location fi xed effects in urban and rural areas, respectively. It is
also possible that residential sorting is more pervasive in some countries than in oth- ers. We conclude that further econometric or qualitative work would be necessary to
better understand the causal pathways whereby wealth affects child cognitive develop- ment, and how these vary from country to country, but information would be required
beyond what is available to us for such estimates.
Finally, we use longitudinal data from rural Ecuador, rural Nicaragua, and rural and urban Peru to analyze possible changes in the wealth gradients as children age.
For this analysis, we limit the sample to children who took the TVIP in all four survey waves in Ecuador 85 percent of children who took the TVIP at baseline,
three survey waves in Nicaragua 92 percent, and two survey waves in Peru 96 percent. Figure 2 shows that in all three countries the wealth gradients that are ap-
parent among four- and fi ve- year- old children are also apparent as these children age. In Ecuador, where the panel has the longest duration seven years, differences
in TVIP scores between wealthier and less wealthy children at 12–13 years of age, when children are of an age where they would be completing elementary school, are
very similar to those found at fi ve- six years of age. In all three countries, there is no
T he
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Table 4 Wealth, Mother’s Education, and Location
Chile Colombia
Ecuador 1
2 3
1 2
3 1
2 3
Urban Areas Wealth
0.78 0.50
0.49 1.23
1.06 0.61
0.87 0.72
0.40 0.06
0.07 0.06
0.09 0.10
0.30 0.09
0.09 0.13
Mother’s education
0.07 0.07
0.06 0.05
0.06 0.06
0.01 0.01
0.01 0.03
0.01 0.01
Location FEs N
N Y
N N
Y N
N Y
R - squared
0.149 0.183
0.197 0.311
0.339 0.732
0.195 0.235
0.352 Adjusted R- squared
0.149 0.182
0.191 0.310
0.336 0.488
0.194 0.231
0.303 Rural Areas
Wealth 0.89
0.65 0.56
0.57 0.49
0.52 1.21
0.91 0.46
0.12 0.15
0.15 0.08
0.07 0.12
0.15 0.13
0.12 Mother’s
education 0.06
0.06 0.05
0.06 0.08
0.07 0.02
0.02 0.02
0.02 0.01
0.01 Location FEs
N N
Y N
N Y
N N
Y R
- squared 0.189
0.223 0.250
0.092 0.112
0.459 0.322
0.386 0.487
Adjusted R- squared 0.187
0.216 0.216
0.090 0.108
0.244 0.322
0.384 0.436
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1 2
3 1
2 3
Urban Areas Wealth
0.95 0.38
0.30 0.12
0.13 0.12
Mother’s education
0.12 0.11
0.01 0.01
Location FEs
N N
Y R
- squared
0.198 0.322
0.397 Adjusted R-
squared 0.196
0.318 0.369
Rural Areas Wealth
0.77 0.63
0.39 0.77
0.50 0.55
0.12 0.12
0.09 0.15
0.14 0.15
Mother’s education
0.06 0.05
0.06 0.09
0.01 0.01
0.02 0.02
Location FEs N
N Y
N N
Y R
- squared 0.119
0.144 0.324
0.139 0.193
0.309 Adjusted R- squared
0.119 0.142
0.240 0.137
0.187 0.280
Notes: The coeffi cient on “wealth” reports the coeffi cient on the fourth wealth quartile. Specifi cation 1 includes only a dummy variable for the fourth wealth quartile; Specifi - cation 2 adds mother’s education, in years; Specifi cation 3 adds location fi xed effects. Clustering of standard errors is done at the community or census tract level Colombia,
Ecuador, Nicaragua, Peru and region level Chile. The calculations of the mean scores give equal weight to each month of age, within a country, and by place of residence urban or rural. Signifi cant at the 10 percent level; at the 5 percent level; at the 1 percent level.
1.5 1
.5 –.5
–1 –1.5
36 42 48 54 60 66 72
Age in Months
1.5 1
.5 –.5
–1 –1.5
54 60 66 72 78 84
Age in Months
1st poorest quartile 4th richest quartile
95 CI 95 CI
First Follow-up
1.5 1
.5 –.5
–1 –1.5
82 88 94 100106 112118
Age in Months Second Follow-up
1.5 1
.5 –.5
–1 –1.5
124 130 136 142 148 154
Age in Months
82 88 94 100106 112118
Age in Months Third Follow-up
Baseline
Ecuador-Rural
1.5 1
.5 –.5
–1 –1.5
36 42 48 54 60 66 72
Age in Months
36 42 48 54 60 66 72
Age in Months
1.5 1
.5 –.5
–1 –1.5
54 60 66 72 78 84
Age in Months First Follow-up
1.5 1
.5 –.5
–1 –1.5
82 88 94 100106 112118
Age in Months Second Follow-up
Baseline
Nicaragua-Rural
1.5 1
.5 –.5
–1 –1.5
1.5 1
.5 –.5
–1 –1.5
First Follow-up Baseline
Peru-Rural
82 88 94 100106 112118
Age in Months
36 42 48 54 60 66 72
Age in Months
1.5 1
.5 –.5
–1 –1.5
1.5 1
.5 –.5
–1 –1.5
First Follow-up Baseline
Peru-Urban
Figure 2 Panel Data Analysis
Notes: Nonparametric regressions of average TVIP score on age in months, by baseline wealth quartile. The bandwidth of the regressions is 7.5.
evidence of catchup. On the other hand, the poorest children do not appear to fall further behind either.
8
IV. Discussion and Conclusions
